Diploma

It depends on your CET/COMEDK rankings, and for the branch you want to join, and also your caste. From what I know, you should try getting a ranking of at least 12000 or higher to join civil branch, 6000 for Electrical and Electronics branch, about 30004000 for Electronics and communication branch. For the more sought after branches like CS and IS, I would aim for higher rankings.

Diploma in Hotel and Catering Management [DHCM]
Fees – INR 28 K /year
Course Duration - 1 Years
Year 1
INR 28,000
Total
INR 28,000
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/hospitality-travel/hotel-hospitality-management/course/diploma-in-hotel-management-and-catering-technology-nips-school-of-hotel-management-salt-lake-city-kolkata-24458&ved=2ahUKEwiBp6rf5qXcAhUMwI8KHTN8CmAQFjAZegQIAhAB&usg=AOvVaw2ZO3C8c_-13qVGP22qMXWb

No, there is no distance Diploma course in which you can get directly into the 2nd year or avail lateral entry benefit.

Follow these links to find your answer:
https://www.university.youth4work.com/colleges-for-mjmc,masters+of+journalism+and+mass+communication
https://www.shiksha.com/mass-communication-media/colleges/m-a-colleges-india
https://www.shiksha.com/mass-communication-media/journalism/colleges/colleges-india.

Approximation is done below:
At the time of Admission:
Rs. 25,000
1st Installment
Rs. 25,000
2nd installment
Rs. 25,000
3rd installment
Rs. 25,000
4th installment
Rs. 25,000
5th Installment
Rs. 25,000
Examination Fee of University is extra.

No, you should have DET for a Diploma in engineering.

Please check:https://goo.gl/Lbws8P.

For admission in BBA, you need to have passed 10+2 in any stream or equivalent. As far as I know, your Diploma will not be considered.